A Class of Zielonka Automata with a Decidable Controller Synthesis Problem

Résumé

The decidability of the distributed version of the Ramadge and Wonham control problem, where both the plant and the controllers are modelled as Zielonka automata is a challenging open problem.
There exists three classes of plants for which the existence of a correct controller has been shown decidable in the distributed setting: when the dependency graph of actions is series-parallel, when the processes are connectedly communicating and when the dependency graph of processes is a tree.
We generalize these three results by showing that a larger class of plants, called broadcast plants, has a decidable controller synthesis problem. We give new examples of plants for which controller synthesis is decidable.